One of the most useful and powerful expressions in After Effects is wiggle(). It randomizes values according to a smooth Perlin noise function.

Prolost Wiggle Position is a handy preset that applies wiggle() to the Position parameter of a layer, and gives you easy control over the expression.

Speed

Controls the speed of the random motion, also known as the frequency of the noise. You can think of this as "wiggles per second."

Amount

Controls the size of the motion, in pixels.

The Customize Group

Use Octaves to specify the complexity of the random motion. Higher values add more levels of smaller, detailed motion to the noise.

Seed controls the random seed used for the motion.

With Include Index in Seed off, the layer's random motion will be the same wherever you stack it. Turn it on and the wiggle will change when you re-sort the layer, which can be handy when applying the preset to multiple layers.